295 comments:

A few classes ago Dr. Susskind displayed the equations for the transformations of coordinates from a rotation of angle theata (I'll use @ to denote theata) asx' = x cos@ + y sin @y' = -x sin@ + y cos@. This preserves sums of squares by which I mean x.x+y.y=x'.x'+y'.y'. To obtain Einstein's equations for motion in one referance frame relative to another we want to preserve the differnce of squares (i.e., we want (x.x-t.t) to be preserved where x is postion and t is time. In his lecture Dr. Susskind said we would guess the equations and then showed they worked.

There is an easy way to see what the equaitons must be without having to guess. Start with the equations of rotation above that preserve the sum of squares and just note that if we lety=it and y'=it' then the sum of squares in terms of x and y becomes a difference of squares in x and t.

So just make the substitution for y and y' as above in the equations for ratation. One easily getsx'=xcos@+itsin@ and t'=ixsin@+tcos@.Now just write sin and cos in terms of exp(i@) and exp(-i@).(i.e., sin@=(exp(i@)+exp(-i@)/2 etc.

This gives immediatelyx'=x*(exp(i@)+exp(-i@)/2)- t*(exp(i@)-exp(-i@)/2)Now just let omega=i@ to get x' in terms of sinh and cosh of omega as Dr. Susskind did.The equation for t' works the same way.

My query is from Cosmology (& Particle Physics). Here is a brief intro:

The early universe was radiation dominated. As you look earlier and earlier, things get hotter. When kT>mc^2 particles of mass m behave as radiation (rather than cold matter), and contribute to the number of relativistic degrees of freedom. [There are some subtleties if you want to do this accurately, but this is the basic idea].

The number of degrees of freedom is thus higher at earlier times. At temperatures ~ TeV all of the particles in the standard model contribute to a total of just over 100 degrees of freedom.

At yet higher temperatures, heavier particles may be expected to contribute.

My question is:What particles are predicted at the GUT temperature and PLANCK temperature by supersymmetry and string (or M) theory ??? How many degrees of freedom do these contribute ???

The number of degrees of freedom at the Planck time may be of particular interest because it determines the current temperature of the background of gravitons left over from the big bang. .... Their detection would revolutionize cosmology in the way the CMB observations have in the past decade.

I have a question about the March 3rd lecture---specifically about the example with the special material that gives E1 and E2 to x and y polarizations, respectively.

You show that if the photon is prepared with polarization in the x direction, nothing happens as it moves through the material. then you show that if the photon is prepared in the / direction, the polarity of the photon rotates thought the XY plane.

Here's what I dont understand. If the photon starts off in the / direction and then rotates thought the XY plane as it moves through the special material, eventually (lets say at time T) it will reach the X direction.

Now, accoring to what you have said, it will be in exactly the same state as it would have been if it had been prepared, at time T, in the X direction. But what seems to happen in the future depends not just on the present (the fact that it is in state |x>) but on the past (whether it was prepared in state |x> at time T, or got there by being prepared in state |\> at an earlier time, and was alowed to evolve to |x> at time T.) In the former case, it will remain in the |x> state, in the latter it will continue to rotate.

Dr Susskind, Just found your blog. I loved "landscape" and couldn't understnad your second book on string theory and information. So I am very happy to have just ordered the book on your battle with Hawking.

I posted the front page of (gr-qc/0503097) by you on my office wall--the essence of science!!

Dr. Susskind.I am one of the "curious people" that you mention in yopur original post on this topic. Please forgive my apparent rambling to begin with, I DO have a point.I have always been a science/technology freak, something of a polymath, and was fortunate to have been born at the start of the space age, which is what first interested me (are you kidding, the moon shot was flat out cool).Anyway, I have also always loved music, and as time passed, I got bored with most current music. (hang in, I'm going somewhere with all this..) I have also always been a voracious reader, and over the last couple of years, I discovered spoken books, which were great replacements for music while I was spending a lot of time in my car. During my search for downloadable literature, one day I came across some particle physics courses "for beginners" and another set on cosmology. I listened to them both many times over,and began to pick up the "lingo" that made other, more detailed talks accessable to me. Then I discovered the KITP web site that has tons of talks and I have not looked back since. I was thrilled to find that there are many other sites out there with similar talks. My original goal was to make it all the way through Richard Feynman's Caltech Lectures, but the more I discover, the more I can't wait for the LHC to start colliding.ANYWAY. My point is this, and I have been mulling this over for a while, and your blog was the first time I had seen it touched upon.There are many people out there just like me, who burn physics MP3 discs to play in their cars, spend all their time looking for new talks (good one from you at the Perimeter Institute BTW) and are soaking up this stuff like a sponge. It's the "music" of the mind. Some of you guys are the rock stars, and some are the new artists (I really like Ayana Holloway Arce {UC Berkeley}, she gave an excellent talk at KITP on the LHC, I loved her enthusiasm).So you are right, and kudos to you for seeing the trend. I'm sorry that I can't do the math, but hey, for now, I'm mostly getting audio, wait until we get some decent streaming video going, I'm sure I'll pick up as much as I need to...Say Hi to Steven for me, his book was also part of my evolution, and I'm glad that you saved the world by winning the war.Regards,Colin Bembridge N.F.D.A.A. Toronto, Canada.

I am a junior high school teacher. One of my students asked me what we will see or feel if we are “light” and I can’t explain. According to the equation, it seems to me that light don’t experience any “time” because it travel along light cone and delta t, x, y, z are all zero. So light itself don’t feel any time or space difference. Is that right?

And what happene if we try to measure light speed if we are “light”? Please tell me. Thanks.

Like all the others have said, thanks so much for holding these classes and making them available on the internet. During my freshman year in collage I changed my major from physics to mechanical engineering and have somewhat regretted that decision ever since. My new year’s resolution this year (40 years after my freshman year) is to learn, and relearn, as much physics as possible. These classes have been a great way to start down that road. I’m 2,500 miles from Stanford so I view all the classes on-line.

While I’m able to follow and understand all the material as presented in the lectures, to really learn the concepts I (like most folks I suppose) need to work some problems. Can anyone recommend a source for problems on the internet or in some books? I’m currently working my way through the special relativity April – June, 2008 lectures.

I saw your interview on CSPAN. It was great. (I was also born in the South Bronx section of NYC but I've never been a plumber.)

Your talk was wonderfully clear. I shut off the TV, believing that I finally understood Quantum Mechanics and Black Holes and your argument versus Hawking's argument and the whole Hawking Radiation thing and the stuff about Horizons and Metaphors and the Point of No Return.

But by the time I got downstairs to tell my Super all that I had learned from the plumber from the South Bronx section of New York, I realized that the magic had worn off. I mumbled something incomprehensible (even now) about String Theory and skulked away.

the derivative of Lagrangian w.r.t. q dot sub i (ith velocity) is called canonical momentum w.r.t q sub i. Now why is time derivative of this is not called canonical force?

Also In cartesian coordinates, its actually force. So as per principle of Least action (PLA), force is the derivative of lagrangian w.r.t q's. So in case of conservative forces, we have kinetic energy always 0, since force = negative gradient of potential energy.

On page 315 of your book, The Black Hole War, you state the basketball will be torn apart at some point by centrifugal force. I believe it has been established that centrifugal force is a fictitious force and what is really tearing the ball apart is inertia. Enjoyed the book.

Monday 11/10/08 GR class: during derivation of the curvature tensor from commutation, the Christoffel symbol appeared as a matrix (two indices) with a coordinate third index. Are these Fock-Ivanenko coefficients? If so, then perhaps this is a path to defining a covariant derivative of a spinor. Here's one reference:http://arxiv.org/pdf/gr-qc/9306006

if anyone is interested this is for you. I have some ideas about using the basic elements for a very powerful fuel. No one ever seems to listen but if anyone is interested that can help contact me at james_jh99@yahoo.com. thanks

I am a lay person currently reading The Cosmic Landscape and watching your internet lectures. My daughter is a dancer, so I enjoyed your dance analogy describing the behavior of strings. I think you and a choreographer from one of the universities in the Bay Area could create a fascinating and educational evening of dance based upon your analogy, a marriage of art and science.

my question is on regards to the relativity of simultaneity problem of referred to as the "andromeda paradox" or the "rietgijk-putnam argument" where two reference frames (a and b) intersect one another in space-time but a is travelling at a significant velocity towards the andromeda galaxy whereas b can be said to be still relative to a. Now if i understand it correctly then the events that are simultaneous to "a" in the andromeda galaxy are in "B"'s future timeline because of the relativity of simultenaety. My question is what happens to cause and effect in this situation, more specifically, if there is and event in the phase that somehow prevents the events in A from ocurring (such as the sudden destruction of andromeda), then how are these events percieved for one would imagine that were something to happen in this phase then the present moment for a would be different than originaly concieved. What does this tell us about cause and effect realtionships? is there higher physics that must be applied or does special relativity provide us with an answer to this paradox?

thank you for taking the time to answer these question, amateur physics students are in your debt.

Wow! Just finished "Black Hole War"! Excellent second-helping, after having read Landscape! Over thirty years of theories, well presented, by the very best, and in the end, a truly surprising result! Peppered with great anecdotes, and a dash of humor, (49 ways to wear a T-shirt!), and woven with the occasional doubt, but the Dr. stuck to his guns, and in the end, his Baby, evaporating with the bathwater, didn't get thrown out! For the record Doc, Oxford was no better than your experience with Cambridge the first time around! Excellent Read! Dave Reid

Ooops! So enamored of the book, forgot to ask my question! In light of the subtlety of the ZPE field at absolute zero,(alluded to several times in Black Hole War) does this mean that even at higher temperatures, i.e. STP there is still not enough to validate the claims of those who seek to sell Zero-Point Energy machines, or as some call them Over-Unity devices?

Dear Dr.SusskindYou mentioned about your lectures on electromagnetic theory that can be found on the web in one of your lectures(which one i can't remember). Can you please tell me where can i find them on the web and is it possible to download them? Your lectures on classical mechanics, quantum mechanics and relativity and field theory are very good, thank you for putting them on the web. I am trying to learn physics again.

Two questions:1) Does anyone know why Prof. Susskind gave up on this blog? He has not participated since spring 2008.2) Did they tape the General Relativity lectures last fall and is there a plan to post them to itunes?

As a new contributer i would like to say well done in taking the time to put your lectures out on You-Tube. I am from the U.K.(Bristol specifically, the birthplace of Paul Dirac), and am following your lectures avidly, (also trying to grasp some of them!). I have two queries:-

1.Will the lectures eventually be released on c.d?

2.Are there any lectures concerning Maxwells development of his electromagnetic theory?

In the case of an extremely massive body, when combined with a small radius, the escape speed can be equal to, or greater than the speed of light.

Let's have a look at the definition, or meaning of escape speed. Derived from studies of ballistics, which, at the time referred to the trajectory of cannon or musket balls through Earth's gravitational field, but, in theory it is that speed at which an object must be moving at the surface of a massive body [such as a star or planet], such that at a distance of infinity it has zero kinetic energy, or no speed; that is, stationary).

These days, the edge of the universe is usually taken as being an acceptable distance. Note that the definition only refers to those things having the property of mass, which can never be accelerated to the speed of light, and not to electromagnetic energy, such as light, radio waves, gamma radiation, etc., which always move at the speed of light in space. Also note that only objects moving along ballistic trajectories are referred to, not rockets or anything else with a means of propulsion, because I intend to return to these points later.

A non-rotating, supermassive collapsar avoids the tidal forces involved otherwise, but, because all stars so far observed have been found to be rotating, it is an almost sure bet that all naturally occuring collapsars will be found to rotate to some degree, but it is theoretically possible that a collision of collapsars or neutron stars can produce one with zero rotation. and, of course, a sufficiently technologically advanced civilisation could produce one, given enough time, simply by directing large amounts of matter at high speed, against the spin, at the equator of an already slowly rotating collapsar.

So, the simplest subject to consider is a non-rotating, supermassive collapsar, (black hole) Scwarzchild radius, (actually, a sphere) also presently being referred to by some as an EVENT HORIZON, may be several light weeks from its centre, minimising the effects of elongation and compression experienced by a robustly constructed and highly powered probe, in free fall and with no radial velocity (speed) with respect to it.

If that probe contained a linear accelerator firing a stream of electrons, or protons away from that centre at a considerable fraction of the speed of light, when the probe is a fair distance away, they may be configured in coded bursts to provide information, and at first would reach a great distance, depending on their initial speed, distance from , and mass of the collapsar.

As it approaches the Schwarzchild radius, the distance they could reach reduces, but even when the Schwarzchild sphere is passed, they could, travelling on a ballistic trajectory, still have the speed necessary to go back through the Schwarzchild sphere to reach a second probe, kept back some considerable distance and easily managing to maintain a stationary position, from which it can either decode or relay the information to us, either by radio or laser messaging.

This is because of a form of relativity; the properties of a collapsar relate to matter, or energy at its singularity. Of course, just within the Schwarzchild radius, different properties apply, but no UNPOWERED object, moving directly away from the singularity at its centre could ever attain the distance of the edge of the known universe, (unless given a gravitational, magnetic, or other assist, such as the pressure of light, or a stream of high speed ions). HOWEVER, it COULD attain sufficient distance as to pass information on the conditions inside the Schwarzchild sphere, as they were at the time it was when it was there, by radio, laser, or by having a highly powered probe approach it, and dock, extracting a capsule, or even taking it in tow. In doing so, information has passed out through the Schwarzchild radius.

Wheeler, Hawking, and many others have reasoned from the specific case of unpowered MATTER, on BALLISTIC TRAJECTORIES, and have erroneously regarded it to apply IN ALL CASES, to any matter, or ENERGY, as well. It has resulted in the creation of a myth of a one way barrier; a kind of unilaterally permeable membrane, which has been termed an EVENT HORIZON.

Hawking had used it as the basis for what later came to be referred to as "Hawking radiation", reasoning that quantum fluctuations near the Schwarzchild radius would cause pairs of virtual photons to be created, some of which would be trapped within that impermeable barrier, but others free to escape. It therefore follows that, if there is no such thing as an event horizon, then there can be no possibility of the radiation type which is dependent on it for its existence.

It's easy to see how so many have fallen into this trap, because the nearest ones are many, many light years away, and from the point of view of someone considering escape speed from within a Schwarzchild radius, the Earth may as well be the edge of the universe. Information is retreivable from deep inside the Schwarzchild radius, and it is dependent only on the technological capabilities of the probes used. Because there is no event horizon, there can be no such thing as a black hole. Therefore I am returning to the old term; collapsar.

The Dollar ($) Matrix, was dependent on an event horizon, as well as the type of radiation which later became referred to as Hawking radiation. Hopefully, this post will clear up a few points; set some minds at rest, and enable clearer thinking about this subject in the future. In the coming weeks, I'll be amending my blog, and posting it on page 2, at http://www.ezy-build.net.nz/~shan_eris I am contactable at: shaneris@gmail.com

In my previous post, I explained how information could be transmitted from within the Schwarzchild radius, using either high speed particles, or a series of probes with powerful rocket motors, (to bypass the restrictions imposed by the definition of escape speed, or escape velocity, which ONLY APPLY to MATTER, on a BALLISTIC TRAJECTORY) and received anywhere outside, even here, on Earth. It is available at http://www.ezy-build.net.nz/~shan_eris

Once it is accepted that it is possible for a particle, or object, to pass through the Schwarzchild radius both ways, it becomes surpassingly difficult to argue that it presents an impermeable barrier to the passage of electromagnetic radiation, which always moves at the speed of light in a vacuum. If, however, it originates just inside the Schwarzchild radius, but is directed away from the singularity, a photon of energy loses energy as it climbs out of the gravitational well, increasing its wavelength, and reducing its frequency (THE ENERGY OF A PHOTON EQUALS THE PRODUCT OF ITS FREQUENCY AND PLANCK'S CONSTANT).

If a probe, just within the Schwarzchild radius, was generating a blue laser beam, and shining it directly away from the singularity, a second probe, following it, but still some distance outside, may well detect it as being red in colour. One further away still may find it was radiating infrared light. One further out than that may only be able to detect it as radio waves. (By modulating that blue laser signal, even using such simple methods as switching it on, and off, using Morse code, information could be transmitted from within the Schwarzchild radius to the immediate outside, and ultimately, to the Earth, through the process of re-transmission at a higher frequency [detecting as radio waves, but re-transmitting as blue laser light] with the mass of the uncharged, non rotating singularity determining how many "booster probes" would be required for information on events occurring within the Schwarzchild radius to reach the Earth).

Eventually, though, for that first probe, transmitting from within the Schwarzchild radius, a distance would be reached such that no signal at all could be detected, because its wavelength would have increased past the size of any antenna. (This raises an interesting issue. As wavelength increases, energy decreases. It appears that some limiting factors must be involved, since, according to the law of conservation of mass/energy, energy and mass cannot be destroyed, merely changed from one form to another. [This, of course, is classical theory, not quantum theory.] The longest radio wavelength which our current technology is capable of detecting is around a kilometre in length.

What happens when the wavelength increases, not only past that which we are capable of detecting, but to the size of the observable universe; possibly even more? What if, instead of a blue laser, it was a very low frequency, long wavelength radio transmitter. Later, I intend to investigate this further, by plugging some figures (starting with a 1 kilometre wavelength; mass of singularity = 1 billion solar masses; distance = 12 billion light years; (a) just within the Schwarzchild radius, & (b) deep within its gravitational well, almost at the singularity) into the equation, but I have many questions, and but few answers, and since none of us knows how long they will live, I have decided to post what I have, now, while I can, so that it is not lost. I am contactable at: shaneris@gmail.com

In one of the classes Dr. Susskind were talking about Hubble expansion and also about Minkowski space time ..I have a query related to above two topics -- 1.In heavy ion collission a comoving frame is used to describe the hydrodynamical evaluation of nuclear matter,the question is what type of coordinate is used here?is it X,Y,Z or R,Theta,Phi.I think it should be polar coordinate as the system has spherical symmetry,am I right? one of the feature of this frame is that particle three velocity is 0 in this frame only it has non vanishing time component,can anyone elaborate on this topic. 2. How Four dimensional hypersurface is defined? as it is necessary for particle emission from the nuclear matter after freezeout. Can anyone help me?

First, I must thank you for your courses. I do a lot of physics 'reaading' on the Internet and your course is the best I've ever run into.

I have just been viewed the third session of the General Relativity course and have come to the section on tensors. It brought back to me a point another Internet physics lecturer had made when he was describing tensors. He said that a tensor was a machine that you put two vectors into out and got out a number. So for instance in the case of the metric tensor in flat space, if you put the same vector in twice, you get the length of the vector which is the same if you choose different coordinate systems. I have read and struggled with the concept of the stress-energy tensor and I would like to know what would be the vectors that would get fed into the stress-energy tensor and what would be the number that comes out? My guess is that the vectors that get put in are the four-vectors of an object moving in curved space-time and that if I put the same four-vector in e.g. feed the stress-energy tensor two identical four-vectors I will get a number which stays the same in different frames of reference. Is that correct? And if so what exactly does the resultant number that the stress-energy tensor spits out represent? Some type of invariant 'distance' in space time?

States that the effects of gravity and acceleration are indistinguishable from one another. The effect of gravity in any physical system is exactly the same as the effect of acceleration.

Although possessing a prodigious imagination, Albert Einstein was largely a product of the nineteenth century in his outlook, considering matters in terms of elevators/lifts, or trains. Unfortunately, it limited his viewpoint. There are at least two ways in which the force of acceleration may be distinguished from that of gravity. Acceleration in a given direction is linear by nature. Gravity, however, tends to be radial in its nature (although I can envisage some exceptions, involving multiple sources).

The following thought experiment can illustrate this point: Consider an extremely long space vessel (for the sake of clarity, by process of exaggeration, let's make it 12,756km, or 7,941 miles long; the diameter of the Earth, at the Equator) with many, many powerful rocket motors, mounted on computer controlled gimballs, capable of sustaining more than one gravity (980 cm/sec/sec, or 32'/sec/sec) along one side, and also powerful side rockets. In interstellar space, someone inside dropping an object, would see it drop perpendicularly towards the side of vessel in which the rockets are firing.

This would occur whether or not that person was on the left hand side of the vessel, the middle, or the right hand side, inside, or in a space suit, outside, on a ledge. Now consider that same vessel, with computer controlled precision, and feedback from accelerometers, and strain gauges; reduce its thrust, and using side rockets as well, causing it to approach, and become stationary above the Earth, so that, if it was to land, its mid point would be on the equator. It hovers at a low distance, somewhat below the peak of Mt. Kilimanjaro. Laser measurement, probably involving mirrors, would show that, in the middle, if an object was dropped, either on to the floor, or from a ledge, to the Earth; it would be perpendicular to both the floor, or ledge, and any flat, level surface below.

At either end, however, any object dropped, (whether onto the floor, or from it, to the Earth) would not appear to fall perpendicularly, to the surface of the beam, or that of the Earth, but angled towards the centre of the beam, at an angle of 45 degrees. This is because of the radial nature of gravity. In the middle, a ball, or a blob of mercury would remain stationary. At the left, or right ends of the vessel, however, once released, they would roll, or flow towards the centre, eventually moving past it, and then back, oscillating back and forth, until friction eventually caused them to stop in the middle. Their initial acceleration would be greater, the closer the vessel was to the Earth. Drawing a diagram may facilitate visualisation of the principle involved.

Alternatively, a series of helium* balloons, supporting a long, straight alloy beam is possibly a more realistic proposition, which bypasses any doubts involving rocket thrust. The middle would hover some centimeters, or inches above the equator, whereas the ends, kilometres, or miles away, would be high in the atmosphere (to achieve maximum length of straight beam). Laser measurement, probably involving mirrors, would show that, in the middle, if an object was dropped, either on to the beam, or from it, to the Earth; it would be perpendicular. At both ends, however, any object dropped (whether onto the beam, or from it, to the Earth) would not appear to fall perpendicularly to the surface of the beam, or that of the Earth, but angled slightly towards the centre of the beam (the shorter the beam; the smaller the angle. In Einstein's time, the difference between the angle of fall in an elevator/lift on the left, middle, and right sides would have been immeasurably small. Even now, it would have to be quite a wide elevator/lift). This effect would also be due to the radial nature of gravity.

Now consider an extremely tall vessel, with a very accurate accelerometer. When accelerating in interstellar space, the acceleration as measured at the top, and the bottom are identical, at one gravity. At ground level, stationary on Earth; either powered, or unpowered (perhaps supported by attached/enclosed helium* balloons) an acceleration of 1 gravity is recorded, but, when measured again at the top, it shows a lesser figure, possibly only .99999 of a gravity (the height of the vessel required to achieve this effect may be reduced in accordance with the sensitivity of the accelerometer used). Because it is further away from the centre of gravity of the Earth, the gravitational force of attraction is less at the top, than at the bottom.

The smaller the scale that is being considered; the more accurate the accelerometer needs to be, to perform its task adequately. Einstein limited himself to an elevator/lift, and of course, in those days such accelerometers as existed were woefully inaccurate in comparison with modern electronic ones. Such miniscule differences between the floor, and the ceiling would have been immeasurably small, and even today, the ceiling would have to be very high, depending on the sensitivity of the accelerometer used.

If the vessel was 6,378km high, at the top, the gravitational acceleration would only be .25 of a gravity. This would apply, whether or not the vessel was powered, but stationary, relative to the Earth or unpowered (of course, the atmosphere doesn't extend that far, so helium balloons wouldn't work that high, and any such vessel would need to have some upper thrusters operational, to support its massive weight, but, being a thought experiment, this need not be taken into consideration; this is merely for the purpose of illustration. In the same way as Einstein could imagine a train moving at the speed of light, we can imagine a vessel of such sturdy construction, that it could rest on the Earth's surface).

Now, consider what would happen to occupants, one at the bottom, and one at the top of such a vessel, using one gravity of thrust to remain stationary, relative to the surface of the Earth, and at sea level, with its rocket exhaust being channeled into deep pits. The one at the bottom would feel one gravity of acceleration; the one at the top, whose head was only several centimetres, or a few inches below the ceiling, would feel a quarter of a gravity of acceleration. Let's replace the occupants with crash test dummies, with inbuilt accelerometers, being filmed, and with radio transmission of data in operation. The rockets fail, for any reason. What happens next? You may wish to work this out for yourself. My explanation follows here**, so don't read it now, if you want to work this out, yourself.

His EQUIVALENCE PRINCIPLE, therefore is a special case, which applies to dimensions on the human scale, that we are generally familiar with, something like how adding two velocities is almost 100% accurate, at the lower speeds familiar to Newton, but wildly inaccurate, the closer the speed of light is approached, requiring RELATIVISTIC MECHANICS to achieve a correct answer.

Although I disagree about some of the statements made by Professor Stephen Hawking, in his book "A Brief History of Time", I nevertheless fully accept his explanation of the effects on an object of compression, and elongation, as that body approached a massive stellar body. If the EQUIVALENCE PRINCIPLE: "The effects of gravity and acceleration are indistinguishable from one another. The effect of gravity in any physical system is exactly the same as the effect of acceleration" was correct, the compression component could not exist. So it can't be dismissed as being merely a case of "a distinction, without a difference". As to the implications, and ramifications of this, however, I am not prepared to speculate, but will leave it for time to tell.

* Hydrogen would be more efficient, in principle, (although potentially far riskier, as shown by the Hindenburg zeppelin disaster) but people are generally more familiar with the concept of helium balloons.

** In the moments immediately following rocket failure, the crash test dummy at the bottom would remain stationary, recording zero gravities, or weightlessness. The vessel, however, would now be accelerating at one gravity, downwards, into the pit. The crash test dummy at the top would impact the ceiling with an acceleration of three quarters of a gravity (the structural strength of the vessel would transmit that one gravity of acceleration along its length, ensuring that the roof moved with that same acceleration. The crash test dummy at the top, however, would be unrestrained, and still record one quarter of a gravity of acceleration. The net difference between the two forces is three quarters of a gravity.

I hope to polish the above, later, and add more to my previous post, but I'll send it off now, just in case of unforeseen events, since it seems to cover the fundamental points fairly adequately.

I've quite enjoyed your lectures and wanted to thank you for putting them online as they've been a wonderful resource.

There was a question that occurred at the 39 minute mark on the third Cosmology lecture concerning the conservation of energy in an expanding universe which I think is a bit subtle.

I found the following in Hartle's book "Gravity" on page 480:

There is some ambiguity but little difficulty in generalizing specific stress-energy tensors to curved spacetime. The conservation law of flat spacetime is no longer satisfied nor should it be. What is satisfied is a natural generalization to curved spacetime (covariant divergence). This relation is called the local conservation of energy momentum. However, it is not a conservation law like the flat spacetime version nor should it be. The energy of matter is NOT conserved in the presence of dynamic spacetime curvature but changes in response to it. The most familiar example is the cosmic microwave background radiation".

I was hoping that in a future lecture you could give an elementary presentation of particle production in the expanding universe such as that described by Parker:

Are the Cosmology lectures online yet?? I can't find them. Also I am trying to find an online type of masters degree in physics or applied physics or maybe a Phd. There are no schools around me that have master's or Phd's in physics. I currently have a 4 year degree in electronic engineering. I live in the southern part of the state of New Jersey. I have looked all over the internet and can find nothing. Would anyone know of a school that would have a masters or phd in physics that could be done in an online fashion. I don't want to have to travel anywhere.

I have been looking at a web site called millennium relativity. It is at http://www.mrelativity.net/Default.htm, Is this good information or a waste of time. The papers seem pretty interesting. I haven't read all of them yet but I have just started to read the papers by the author Kristos Mavros.

I have just started looking into the General Relativity lectures by Dr. Susskind. Can anyone please suggest me book or video podcast to follow the mathematics that Dr. Susskind discussed in the third lecture. I want to know more about the mathematics involved and how it works. I have basic proficiency in calculus.

In the Cosmology 3 video when constructing the FRW equation the Prof uses a sphere of radius 'a' and gets a 4/3*pi*a**3. However, when determining the energy density 'rho' he uses a unit cube to give M/a**3. Why a﻿ cube and not a sphere? A sphere would lead to rho being 3*M/4*pi*a**3. The FRW would then reduce to 2*M*g/a**3 - k/a**2. I assume I have misunderstood something so am interested in any correction.

Dr Susskind,First thank you for your educational volumes on the “Black Hole War” and “The Cosmic Landscape.” Both of which I appreciated immensely.In chapter 2 of “The Cosmic Landscape” you talk of the Mother of All Problems.

Here is the outline of a solution which has great relevance to the holoscopic viewpoint.

Solution to the Vacuum Energy Density Problem

Stephen Hawking showed that for a black hole the minimum increase in energy was that of a photon of wavelength equal to the event horizon diameter and that this produced an increase of one Planck unit in the event horizon surface. This indicates that only integral increases of Planck units are allowed on any surface; so energy, entropy or bits of information are quata and that the energy required for each additional bit decreases inversely as the diameter.

QM calculates the average energy density of a vacuum to be about one Planck mass per cubic Planck length. This is only true for a uniquely observed point in a vacuum, or for the only point in a vacuum, the second adjacent point would have a minimum energy of 1/√2 times this amount, the third 1/√3 as each new area would be resolved by the lower energy of a longer wavelength photon. The total energy is the sum of (1+1/√2+1/√3+…) times the original energy.

As both the entropy (information density) and the energy required to produce that increase both decline with increasing diameter the overall average energy density falls as the inverse of the surface area (as 1/R^2.)

Average energy vacuum density (Ev) for a volume enclosed by q Planck unit squares of surface.

Ev = e'.∑ n=1,n=q(1/√n).6/(π.(√q.d' )3)

Where e' ≈ Planck energy, d' ≈ Planck length,

For large q Ev ≈ 12.e'/(π.d'^3.q)

For a vacuum the same size as our visible universe (+/- 80 billion lightyears) this comes to

Ev ≈ 1.5x10^-25 J/cm3

This is a factor of 10^10 less than that observed for our universe but this calculation is for a pure vacuum. Any mass, energy or field present will increase this significantly.

This is still a much better result for quantum gravity calculations than the 10^120 excess as of present.Comments?

... and by the way, you once said in your lecture that "eigen" is German for proper, and someone in the audience disputed that. However, eigen can several things, and you're absolutely right: in this case its German meaning is "proper".

I watched the first lecture of special relativity (and a bit of the second), but before I continue, some things need to be cleared up. I have a question concerning simultaneity. I will use two different thought experiments to approach my problem.

Experiment 1:We have two identical trains riding with a constant velocity v relative to each other. There is one observer in the middle and both the right and left side of the train. The observer in the middle of train 1 is holding a lamp just outside the train. At the moment train 1 rides exactly next to train 2, the observer in the middle of train 2, pulls the lever of the lamp so that the lamp goes on.

O1----------O2----------O3 ---L---U1----------U2----------U3

The result: a beam of light going to the rears of the trains and a beam of light going to the fronts of the trains. (ignoring the beams going in all other directions). The observers on the rears and fronts of the train raise their hand when they see the light.

We ask ourselves the following question: "What sees the middle observer in train 1?".The answer: He sees that the observers in his own train raise their hand at the same time. He also sees that the observers in the other train don't raise their hand at the same time. Namely; the rear one first and the front one after, for the train is moving relative to the other.

The middle observer in train 2, will notice; in his train the observers on the rear and front raise their hand at the same time and in train 1 they don't.

Experiment 2:If we now go to Einstein's example; the following video: http://www.youtube.com/watch?v=wteiuxyqtoM ...Here is stated that the observer on "earth", the man standing outside of the train sees the flashes at the same time. He also sees that the woman in the train does not see them at the same time. If I compare this situation to the example above here I assume that the woman also sees the flashes at the same time, but that she predicts the man does not. But that is not what Einstein said apparently. Einstein said in this example: The man in his reference frame sees both flashes at the same time, the woman doesn't see both flashes at the same time in her reference frame.

Isn't that contradicting? I have been reading those thought experiments over and over again, but I can't find why the situation in the first experiment can't be compared to the situation of the 2nd. My question now is: “why am I thinking wrong?”.

I am sorry for my unprofessional language. I'm dutch and might have missed a few crucial facts in my explaination.

Dr. Susskind, I have read your book "Cosmic Landscape" and enjoyed it. I am now reading "Black Hole Wars" My question is on page 388 in the Polchinski section about membranes.You speak of D0, D1, D2, etc. and say the membranes are made of MATTER, What type matter??? What are the membranes made of???Thanks, Alex

Only a few hundred years ago people thought that anyone travelling at more than 25 miles per hour (40 kph) would die from the stress on their bodies. We now know that it is possible to travel at many thousands of miles or kilometres an hour without experiencing any stress whatsoever.

For many years it has been the dream of scientists and sci-fi writers to utilise the apparent slowing down of the passage of time on nearing the speed of light, known as THE TIME DILATION EFFECT, as a way for a vessel to travel to the stars within the lifetime of its crew. In their book "Intelligent Life in the Universe", by L.S. Shklovskii and Carl Sagan (ISBN 0 330 25125 2 , ), p444, they even provide a graph showing how many years would be required to reach various interstellar destinations at a uniform acceleration of either 1,2, or 3 gravities ( 1g = 980 cm/sec squared, or 32'/sec squared ).

Unfortunately, it has fallen to me to explain how the laws of physics prevent unaltered humans like us (i.e.; non cyborgs) from attaining such a long sought goal. Firstly, it is important to understand the difference between mass and weight; e.g. a person weighing 60 kilos on Earth would only weigh 10 kilos on the Moon, but their mass would not change. On an unpowered interstellar vessel that person would have zero weight (weightlessness), but still have a mass of 60 kilos, mass being that property of matter which resists acceleration.

At very high speeds, well over half the speed of light, the situation changes, and that person may have a mass of 120 kilos, or 180 kilos or much, much more, depending on the speed attained, even if the vessel was unpowered at that time and the person was weightless. The Newtonian laws of physics still apply, however, at every instant, irrespective of whether the vessel is accelerating or not; particularly f = ma ( force equals the product of mass and acceleration ).

They may be said to be in an inertial frame of reference. The human heart is a muscular pump, which pumps blood, a liquid with a specific gravity, or density, which is slightly greater than 1, (1.05 - 1.06) or 1kilo/litre at low ( Earth or current technology rocket ) speeds. As the speed of future vessels increases, however, not only the mass of the occupants, but also the density of their blood increases, almost immeasurably slowly at first, but then rising more and more, on an exponential type curve.

The heart, though, is a muscle, which is powered exactly the same as every other muscle in every known animal; by the chemical breakdown of the AdenosineTriPhosphate molecule (ATP) into AdenosineDiPhosphate (ADP), providing animmutable amount of energy. At around .8c, or 80% of the speed of light ( ref: COSMOLOGY, p.57. Jim Breithaupt, 1999. NTC/CONTEMPORARY PUBLISHING, 4255 WEST TUOHY AVENUE, LINCOLNWOOD, ILLINOIS.60646-1975 USA, or any good book on relativity ), the mass of a person would double.

But, at any speed, f = ma still applies, therefore; as the mass increases, so does the density of the blood and the speed at which blood can be pumped through a heart reduces accordingly, because it only has a limited amount of biochemical energy available. A lowering of blood pressure would occur, until, even in a young and physically fit person with a large heart (like a long distance runner), unconsciousness and with increasing speed, death would result.

The problem would still exist even under low acceleration or zero g (weightlessness), and the only solution would be to reduce speed. Not only the heart, but also other organs would be similarly affected, although the effects could (for a time) be ameliorated by reduced acceleration; any acceleration in the direction of flight would result in further increase in mass, adding to the problem.

For example; at about .8c and an acceleration of 1 gravity (980 cm/sec/sec), a person who weighed and had a mass of 60 kilos on Earth would weigh 120 kilos and have a mass of 120 kilos, but if the acceleration was reduced to 1/10th of a gravity, that person would still have a mass of 120 kilos, but a weight of only 12 kilos, easing the burden to some extent. Using an artificial heart, like a more advanced version of the Jarvic 7, would help for a limited time, as would a computer controlled variable pacemaker.

With the recent advances in the growing of organs such as skin or even livers in the laboratory, however, it may become possible to create organs which are specially adapted to high density fluids, thus allowing the attainment of slightly higher speeds. Some of the limiting factors would be the lungs and blood vessels, particularly those of the brain, where cerebral haemorrhage would become increasingly likely with any further increase in speed, due to the "hydraulic ram effect". Other problems envisaged would include crew mobility, as well as the ingestion of food and the elimination of waste.

The crew would have to constantly retrain themselves during the acceleration phase, in how to move around. An analogy is that of a scuba diver in a heavy metallic suit, which contains enough air so that it is easy to stand on one hand, but very difficult to start moving (due to inertia), or to stop or change direction, once in motion (owing to momentum).

Accidents and injuries would be common at first, even under low acceleration. Under such conditions I would expect that short, muscular people would have a distinct advantage. It would be due to the greater leverage involved, with shorter bone lengths, in the same way that there are no very tall Olympic weight lifters.

Well spotted, Nick! It will be interesting to see if you find any others. I believe that I did, but nobody else seems to have done so (I was educated in the concept of centrifugal force, as well, so I'm not counting it). It's good to see someone else reading with a critical eye. Certain allowances should be made for elderly professors, however, and everyone makes mistakes; I certainly do. I'll get "The Black Hole War" from my library, and note the abovementioned erroneous statement, should you fail to find it.

String theory is a developing branch of quantum mechanics and general relativity into a quantum theory of gravity. The strings of string theory are one-dimensional oscillating lines, but they are no longer considered fundamental to the theory, which can be formulated in terms of points or surfaces too. Leonard Susskind is a pioneer in this field. I am a college sophomore with a dual major in Physics and Mathematics @ University of California, Santa Barbara. By the way, i came across these excellent physics flash cards. Its also a great initiative by the FunnelBrain team. Amazing!!!

GR-curvature-commutator: We derived Riemann Tensor by taking the commutator of the covariant derivatives and it's neatly done in nice and simple operator notation. However, there should be a torsion tensor if we are considering general connections not Christoffel. What's wrong with the derivation? How can we recover the torsion component and still, in the neat operator notation?

I am having certain naive doubts in string theory concepts. What I have learnt from certain documentaries (http://www.youtube.com/watch?v=zQLfRkzgMUY and remaining other parts)that:

1. All the matter is made up of tiny strings of energy. They can be open ended strings or closed loop strings (like a rubber band or a rubber cut in half).

2. These strings can vibrate in any way (in 6 dimensions) and their vibrations produce phenomena like charge or mass etc. which can be experienced in physical world.

3. A particular type of vibration gives rise to a particular physical behavior for example – charge. If the string is vibrated in other manner, other physical behavior can be observed for example – mass.

Now based on these three points, I have certain doubts in my mind:

1. Since the manner in which a string is plucked, different characteristics will be shown it will show. Is the frequency of the oscillation deciding the characteristics of that particle?

2. If it does, will overlapping of two similar strings, differing by a small frequency, generate BEATS as observed in the case of real strings of violin etc? (I am pretty sure that beats should be formed in those strings, and I feel that these can be one of the proofs that strings exist).

3. What are beats in the case of these strings? Can a physical phenomenon like variable mass depict beat formations? A particle named ‘Z°’ shows a variable mass phenomenon (mass and half life are inversely proportional). What is the reason behind this?

4. And if it does not happen, what happens when a string twists to form an ‘ 8 ’ from ‘ 0 ’? if the two halves of the string have more tendency to twist, what will they do? Will they repel each other like an actual rubber band or those two strands of energy pass through each other?

Please do help me clarify if any of my previous assumptions is wrong...

I am having certain naive doubts in string theory concepts. What I have learnt from certain documentaries (http://www.youtube.com/watch?v=zQLfRkzgMUY and other 11 to follow) that:

1. All the matter is made up of tiny strings of energy. They can be open ended strings or closed loop strings (like a rubber band or a rubber cut in half).

2. These strings can vibrate in any way (in 6 dimensions) and their vibrations produce phenomena like charge or mass etc. which can be experienced in physical world.

3. A particular type of vibration gives rise to a particular physical behavior for example – charge. If the string is vibrated in other manner, other physical behavior can be observed for example – mass.

Now based on these three points, I have certain doubts in my mind:

1. Since the manner in which a string is plucked, different characteristics will be shown it will show. Is the frequency of the oscillation deciding the characteristics of that particle?

2. If it does, will overlapping of two similar strings, differing by a small frequency, generate BEATS as observed in the case of real strings of violin etc? (I am pretty sure that beats should be formed in those strings, and I feel that these can be one of the proofs that strings exist).

3. What are beats in the case of these strings? Can a physical phenomenon like variable mass depict beat formations? A particle named ‘Z°’ shows a variable mass phenomenon (mass and half life are inversely proportional). What is the reason behind this?

4. And if it does not happen, what happens when a string twists to form an ‘ 8 ’ from ‘ 0 ’? if the two halves of the string have more tendency to twist, what will they do? Will they repel each other like an actual rubber band or those two strands of energy pass through each other?

In the following lecture: http://www.youtube.com/watch?v=BjUJra50bcY&feature=PlayList&p=CCD6C043FEC59772&index=3 (lecture 4:special relativity) proff. Susskind wrote down the euler-lagrange equation (ELE) of motion, describing a field. what was the difference between the 1st ELE and the second one?

Hello Dr. Susskind; I am a physics student, I have a question regarding whole QM I think, but in particular in the case the rel. QM. How do particles are created from the kinetic energy of another one? Is a photon a bound state of electron-positron? Even though I contradicted myself by thinking in this case they have mass and wouldnt have the maximum speed c.

Refering to Prof. Susskind's lectures on the net on special relativity (classical field theory) lecture no. 2.Following the lecture were classical string equation was derived by modeling the string as continuous masses & springs distribution, It is not cleare to me whether there is any restrictions on the vertical displacement.Professore Susskind did not mentioned any.On the other hand the same D.E.is often derived by applying equilibrium on a segment of the string in this procedure the vertical displacement is restrictedto be small compared to the original string's segment.what is the explanation for the apparent different assumptions along the two procedures

I've been following the quantum mechanics lectures on Itunes. They are excellent, but it would be great if there were some written material and/or text to supplement the lectures. Are there any suggested readings to go along with these lectures?

I have a question from relativity ,searching the answer .Suppose I saw my fried in the morning . He told me that the all dimensions are reduced to one third ,ie length mass time etc are reduced to one third.The entire universe shrunk into one third Will I feel it?

dear prof. Susskindif we calculate the time (Tb)of a clock "B" that move to a velocity +v fowards and comes back with velocity -v(respect a clock A fixed) with Integral(Sqrt(1 -dx^2/dt^2))dt we find that is of Tb < Ta.But if we immagine to take the reference in the clock "B" that clock looks the clock "A" going fowards with velocity -v and go back with velocity +v. Now Ta < Tb (versus Tb<Ta) because (?) the situation is dual (where is my mistake ?)thanksFabiano ManzanMotion control system integratorfabiano.manzan@art-of-motion.it

Its said that a star converts hydrogen to helium and then to carbon, and on a late run it dies as it's nuclear fuel expires. (Basically the star doesn't have that amount of heat to progress in its nuclear fusion.)The star dies due to its contraction of its own gravitational field.

My question is:During the course of nuclear fusion(when it's blue, red star) the gravitational pull is not that much as the star doesn't have "HEAVY" elements (like carbon etc). The above is the reason that the star doesn't contract that much when its blue,red than when its stationary( meaning that no nuclear reaction are taking place) ? right!!

In the quantum mechanical experimental measurements when the photons are released do they have one frequency? If so what is it? If there is more than one frequency is there a relationsip between it and some other parameter(s)?

dr.susskind i fear i am not nearly as well versed in physics as some bloggers and so my query is acordingly simple: can you explain in the most literal sense the actual functions of w and z bosons as far as the resective roles they play in the electroweak theory i am perticularly bothered by were particles of that wieght come from and how they interact with other particles?

dr.susskind i fear i am not nearly as well versed in physics as some bloggers and so my query is acordingly simple: can you explain in the most literal sense the actual functions of w and z bosons as far as the resective roles they play in the electroweak theory i am perticularly bothered by were particles of that wieght come from and how they interact with other particles?

dr.susskind i fear i am not nearly as well versed in physics as some bloggers and so my query is acordingly simple: can you explain in the most literal sense the actual functions of w and z bosons as far as the respective roles they play in the electroweak theory, i am perticularly bothered by where particles of that weight come from and how they interact with other particles?

In"The Black Hole War, , Leonard Susskind states "Einstein found that the very short wavelengths (high frequency)less than a single photon. So the very short wavelengths carry no energy and the ultraviolet catastrophe ceased to exist."

Does this mean waves without photons exist? How does this square with E=hv for UV, Xray, Gamma Ray waves?

Hopefully someone much smarter than I can shed some "light" on my confusion.

First write out the covariant derivative of the metric tensor and permute the indices (i.e., a->b, b->c, c->a) twice to get the equation in 3 forms.

Then note that the covariant derivative of the metric tensor vanishes and that the covariant indices of the metric tensor and christoffel symols are symmetric. You can then use basic algebraic methods to solve for a particular christoffel symbol only in terms of the metric tensor.

Ye Gods, Prof., do you go through all these - it's the first time I've been on your blog, but please allow me the temerity to thank you for your terrific learnoutloud quantum mechanics lectures. It takes me back many years and, when I get my head around it again, perhaps forward a few centuries (well you never know!)

Ye Gods, Prof., do you go through all these - it's the first time I've been on your blog, but please allow me the temerity to thank you for your terrific learnoutloud quantum mechanics lectures. It takes me back many years and, when I get my head around it again, perhaps forward a few centuries (well you never know!)

In his book 'the black hole war' Dr.Susskind states that the war is over. Though I really enjoyed reading Dr. Susskind's book (and his online courses) a lot it seems to me that the war is not over yet: Hawking surrendered allright ... but Penrose didn't. The arguments used to 'win' by Dr. Susskind's camp depend on string theory to a large extend... and that is not even a theory according to a lot of renowned scientists (like João Magueijo, Penrose,...).The problem with information loss in black holes is all about the principle that quantum systems should evolve in a unitary way according to quantum theory... but making observations somehow destroys this unitary evolution and collapses the wave function to the value that was measured. According to Penros the unitary evolution is not enough to explain the observation of quantum systems (seems to me that he' s right !) and so ... unitarity should not be 'conserved' when quantum systems are observed to fall into a black hole...

Anyway...in his new book 'Cycles of time' Penrose keeps saying that Hawking should never have surrendered. Loosing unitarity due to influence of strong gravitational fields is not a problem ... says Penrose.

I do not know who is right, I do know that both Dr. Susskind and Dr. Penrose are respected scientists that continue to disagree ... Perhaps they are not really 'at war', but they do disagree about the question if quantum systems loose information in black holes or not. As far as I'm concerned: the issue is far from resolved.

Isn't true that the stability of orbits is only presumed by Law, and that each and every change causing the measured instability of orbits, such as changes in temperature, body diameter, the effects of other orbiting bodies, etc. have not all been measured simultaneously with certainty. Could the uncertainty in the stability of orbits make any significant impact over vast time scales. Not only including the uncertainty in the instability of orbits, but also those uncertainties in the second order deletions in approximations, such as tidal forces, and how these render it necessary that these orbits are in fact unstable, since the stability in the approximations are the only and unique conditions whereby such stability results.

Hi Dr Sussking..well I have started to watch Einstein's Theory Lecture and it is very interesting that you beginning with the concept (or notion) of Force and mass they were "thing" of reality. Considering we can not see forces and only their effects in space and time, is not it time for a revision (as it did Mach) of these concepts? (excuse my English).

You should check out the amazing flashcards that funnelbrain has to offer! I find them to be a very useful educational tool. I never thought that flash cards could be so useful but, they are! And they're a great project to work on with a partner.

This is all very complex, and I am still using flashcards to learn and study physics. In addition, Thank you for taking the time to place your video lectures on youtube! I have mad some flash cards from your clips on youtube that have greatly increased my understanding! Also, as another poster mentioned, string theory. Have you any video on this subject? -Cheers!

Electron pair production from photons requires a "scalar real field" (photons) to be broken into a pair of "complex conjugate fields" (electron + positron)

It's fairly simple to imagine 2 scalar photons fields approaching with fields 90 degrees apart. At the point the cross, they are almost exactly the same as the complex field required for the electron.

This is supported by the fact that pair production always requires 2 photons.

Also since the energy of the photon feilds equals the energy of the rest mass of the electrons, the resultant electrons should have 0 velocity. The extra energy must be coming from a "blue shift"as he fields approach.

I dont see how you need extra dimensions for the complex field, when its just a vector field with a non zero curl in "normal space", like a whirlpool.

Anyway, awesome awesome lectures, i have special interest in the equivalence of light and matter.

I really think 2 real scalar fields combining in quarature to form a complex field is a real go-er!

It also strikes me that adding the resultant complex conjugate fields produces a real field of twice the real amplitude. Which is equivalent to the super position of 2 photons. Which is what you get from electron/positron anhilation.

The next thing to do is to prove that electrons are contained photon fields bound in quadrature and we can split the nobel prize?

Dear Prof. Susskind,as many others here I found your classes on iTunes and started following them,Thanks for your outstanding work, as witnessed by the many comments that keep landing on this blog.I dedicated an article on my blog as well, hoping it will serve to wake-up the interest in phisycs and science in general, in my country, here is the address:

The group-theoretic derivation of the Lorentz-transformation made me ask some questions.

First of all, it seems that laws of nature can be described as group operations. I think it is a fundamental property if we consider that science should be internally consistent.

If I correctly understand things, the nature of the Lorenz-transformation partitions objects to three different sets: objects that cannot travel faster tnah light, object that travel at the speed of light, and object that travel above the speed of light. Is there any theoretical limitation that permits a Universe to exist, where every particle is either superluminal or travels with c? So it would be an "opposite" as our observed universe.

Lecture 2 of General Relativity – If I understand correctly, the equivalency principle states that gravity and acceleration is the same physical phenomena. This raises a question in my mind on the behavior of a charged body at rest while supported in a gravitational field. If it is experiencing the acceleration by being in the field, why doesn’t it emit electromagnetic radiation?

OK … of course, after I posted the question, I had a thought. If the charged body at rest, then it is in the same frame as its surrounding? Therefore the charge doesn't have a delta that allows it to “see” the acceleration. Is this though on track???

in the part of obtaining the newtonian approximation formula from geodesics, what is the meaning of the christoffel's symbol in the expression with the lower indices?Is it the neta tensor?or something else?

Dr. Susskind,I am a Mechanical Engg. but very keen to learn physics.I was going through your lecture over special theory of relativity(lec-1),there you defined proper time as following,dT^2=dt^2-dX^2,T=proper time..My question is why the dimensions of both sides of the equation are not matching i.e left side is time(I suppose) & no idea about right side!In this context I want to tell you that I 'm novice in these field of physics..if there is any misconception in my idea please let me know that.

Dear Sourav,The dimensions on the two sides of the equation are the same. It's just that susskind works in units in which the speed of light equals one. that is: c=1. if you add the speed of light to the equation you get the equation:dT^2=dt^2-(dX^2)/(c^2) which if you observe has the same units in both sides.

Hi Dr.Susskind. I'm an 11 - year old girl doing a school project on String Theory. We are going to be having a "fair" where we present our projects to other students and parents. I first found it confusing, and other people probably will, too. What tips can you give me to present this to people, using my tri - fold board?Thanks!

In lecture 3 on special relativity you said that -- "For a light moving in different kinds of material, the time it takes for the light to travel from one point to another is the shortest possible time."

But I have heard about cerenkov radiation whose definition is " Electromagnetic radiation which is emitted when a charged particle (such as an electron) passes through a dielectric medium at a speed greater than the phase velocity of light in that medium."

so doesn't this particle travel the distance between two points in the shortest time ?

respected sir,physics is the subject the more u learn the more r u confused.my question is -it is believed that he universe came to existence after the big bang,before big bang universe was supposed to a huge ball of mass and fire.the whole of it is composed of gases and the whole mass was concentrated due gravitational pull.what led to big bang.what was the internal condition just before big bang happened.can u verify these theory

I am following the lectures on Quantum mechanics. In the third lecture a an example is given of a particle that can have a 1 dimensional position x. Then it is derived that the eigenvectors for the position operator are the dirac delta functions.

My question is what is preventing you from setting the eigenfunctions to constant*(dirac delta function).

I found your lectures only recently and find them most informative, but I'm only halfway through ( I'm a chemist ).

So I have a question: you try to explain everything by a least action priciple. Only in your gen. rel. lecture, you fully apply the standard way ( tensors, cov. deriv. etc ) although there exists also a least action method ( -> hilbert action ). I really would have liked that somebody explained that to me in your very lucid style ;-)

Sir, in your lecture1 of STR Q1)when you said primed frame is moving with velocity V, do you assume that it's moving eternally with this speed (i.e. from t=-Inf to +Inf). But for practical purposes it is not the case and hence the acceleration of primed frame is unavoidable(may be for a very short interval of time). So during that interval GTR comes into picture; doesn't that affect our further derivation? I mean doesn't it alter any property of the space-time.

Q2)you wrote x2-y2=0, x'2-y'2=0 (:p statement) and then you used x2-y2=x'2-y'2 (:q stmnt). Although p=>q but q doesn't necessarily imply p, so is not the derivation following it logically inconsistent.

Sir, in your lecture1 of STR Q1)when you say primed frame is moving with velocity V, do you assume that it's moving eternally with this speed (from t=-Inf to +Inf). But for practical purposes it is not the case and hence the acceleration of primed frame is unavoidable(may be for a very short period of time). So during that interval GTR comes into picture; doesn't that affect our further derivation? I mean doesn't it alter any property of the space-time geometry. Q2)you wrote x2-y2=0, x'2-y'2=0 (:p statement) and then you used x2-y2=x'2-y'2 (:q stmnt). Although p=>q but q doesn't necessarily imply p, so is not the derivation of following it logically inconsistent.

Dr. Susskind, I've been thinking about the "double slit experiement" and what it's ultimate conclusions are if you take the theories of multiple universes to its extreme.

Is it possible that there is only one particle? I'm not talking Higgs-Boson. I'm talking one particle - and all we see and all we know about in this universe is really an interactive portion of an infinite multiverse based on one single particle. It would partially answer the cause of the big bang - or how it went about. It would also partly answer a lot of deeper questions... like why am I here?

Prof. Susskind very often specified the Higgs field by means of the expression (I’m going to use LaTeX notation)

\fi=\rho e^{i\alpha}

The homogenous variation of the \alpha would be connected with the Goldstone’s bosons, whereas the variation of \rho would be connected to the Higgs particles, as the latter are the quantum excitations of the “oscillator” around the point in the \fi field you call “f”. You very often make the assumption that the potential energy entering in the Lagrangian, as a function of \fi^*\fi, is so steep that in your applications you may turn \rho into the parameter “f” which is just the magnitude of \fi at the minima of potential energy all along the circle described by the \alpha variation and, in case of symmetry breaking, the field would shift from the zero value, to f e^{i\alpha}.

Now is the question… Higgs’ bosons are the quanta associated to the excitation of the field and, provided there is not enough energy, they are not generated; but… what about the zero point vibrations of the field that a quantum calculation should foresee? The higher is the steepness of the potential function around f, the higher should be the energy of the ground state; so that the energy of the vacuum (in the case of symmetry breaking) should be significantly higher than the energy at the minimum of the potential. Am I right? And, in case, does this zero point vibration play any role in the theory, or can we easily get rid of it by redefining the position of the zero of the energy?

Hi Dr. Susskind, I was watching a tv show about your debate about black holes with Stephen Hawking. It got me thinking. I assume this has been exhausted already but I'll give it try.

What if a black hole is not a singularity but something close to it and not enough to unify the 4 known forces in total. It should then be possible to ultimately destroy it releasing the trapped holograms so they can eventually be observed by an astronomer.

But ultimately could the event horizon of the singularity of what caused the Big Bang also have trapped information of the Universe before ours and then released it?? Maybe masked by the cosmic background radiation?

I just read as I was writing this that there may be possible evidence of this.

Special Relativity:~~~~~~~~~~~~~~~~~~It does not seem at all obvious to me that the Lorenz transformations are the only transformations that exist that meet the requirement that 2 2 X-(Ct) is invariant. Surely there must be many transformations possible if that is the only criterion?

Two massless particles, 1 and 2, are created simultaniously at the same point in space and moving at right angles to each other, both moving at the speed of light. Particle 1 travels 1 light year and is reflected back to particle 2. How long, in particle 2's time would it take for particle 1 and 2 to combine?

I found this site drifting around on the net. I found it very interesting. I have always found science and physics interesting, Though i am only a high school graduate.

I have two questions i have never been able to have explained to me by the people who i come in contact with. Perhaps some one who might see this,and of higher learning maybe able to answer them. Perhaps some one from Stanford University .

1.Why do the sums of the multiples of 9 add up to 9.Example.9x9 = 81/8+1=99x5=45/4+5=9 or 9x4563=41067/4+1+0+6+7=18/8+1=9 or 9x78963=710667/7+1+0+6+6+7=27/7+2=9.Any multipal of nine comes out to nine.Why is this. Is this just a mathematical anomaly .Or is their a mathematical reason for this.

2.Why when looking at revolving object, such as an airplane propeller. Or a wheel spinning at high speed. When the revolving object looses velocity it will appear to revolve backwards at intervals.Is their a physical property or reason for this. Or is it just a trick of observation.

Any one who might know the answers to these question can relay them to me atjoezeke@yahoo.com

I found this site drifting around on the net. I found it very interesting. I have always found science and physics interesting, Though i am only a high school graduate.

I have two questions i have never been able to have explained to me by the people who i come in contact with. Perhaps some one who might see this,and of higher learning maybe able to answer them. Perhaps some one from Stanford University .

1.Why do the sums of the multiples of 9 add up to 9.Example.9x9 = 81/8+1=99x5=45/4+5=9 or 9x4563=41067/4+1+0+6+7=18/8+1=9 or 9x78963=710667/7+1+0+6+6+7=27/7+2=9.Any multipal of nine comes out to nine.Why is this. Is this just a mathematical anomaly .Or is their a mathematical reason for this.

2.Why when looking at revolving object, such as an airplane propeller. Or a wheel spinning at high speed. When the revolving object looses velocity it will appear to revolve backwards at intervals.Is their a physical property or reason for this. Or is it just a trick of observation.

Any one who might know the answers to these question can relay them to me atjoezeke@yahoo.com

Leonard:Thank you so much for your lectures. I'm from Argentina. I'm 21 and currently studying Chemical Engineering and already know a bit of Calculus and Algebra. I started watching some of your videos about Quantum Entanglement, Special and General Relativity, but I need some kind of guide to understand modern physics and put all the pieces together. What series of videos should I watch first? For example I read somewhere that Special Relativity is needed to understand General Relativity. Am I right? Thank you so much!!

If your problem is that it seems contradictory to say that a photon has no mass but has momentum, you have to keep in mind that the classical definition of momentum = mass * velocity does not hold for relativistic particles.

In special relativity momentum = gamma * mass * velocity where gamma = 1/(1-(v/c)^2)^(1/2). If mass = 0 p does not nessecarily = 0 if v=c we get 0/0 which is indeterminate. So;

If you want the relationship between energy, mass and momentum use:E^2 – (p*c)^2 = m^2*c^4

Does light have any mass? (even infinitesimal) I heard it had "no mass." If so, why is it called 'light'? What is the etymology of the word 'light'? I remember something about solar sails propelling long-distance spacecraft. How could light provide a push, if it has no mass?

Is there such thing as an antigraviton? antiphoton? Why are the words for serious and humorous involved in physics? Is levity (light-heartedness) a source of levitation? Is gravity a matter of grave concern? Why should it bring me down? Death is an anagram of 'hated'.. And finally, if "nothing can escape a black hole, not even light", how do the gravitons escape (you said two black holes can attract)

Dr. Susskind, Cosmology question: What caused inflation to end? I saw an article on the concept of hybrid scalar fields so instead of the one scalar field there is also a second one that basically oscillates to a point of tachyonic instability once the original field drops below a certain threshold. Do you agree with this hybrid scalar field theory?Second question is regarding metric tensor in general relativity. So based on cosmological constant there is no pure minkowski space because there is alway a little vacuum energy to cause curvature even if no mass is present. True? Also, some physics "play" with the metric tensor to create warp engines my merely making the coefficient of metric tensor functions of dx, dy, dz, and dt. You can moosh space up any way you want basically are there any limits with this or just the imagination.Lastly, I have a theory that the universe could within a sub heisenberg constant unit of time be collapsing a re-expanding periodically, but we would not detect it because of the small time slice with which it happens. This is how space travel could exist. To catch a ride as universe collapses and expands.Thank you,Fred De Prosse (UC Davis engineering, 1985)

I know these questions are stupid. Don't worry about the details a simple yes or no will suffice. Could the dark matter be dark cause its inside black holes? Could the halo that surrounds galaxies, discovered by its effect on light, be something other than the missing matter?Could the matter that's missing be hiding inside black holes? Also on to a different subject. The farther you look into the cosmos the farther back in time you are looking, and the farther you look the faster things are moving away from us. Wouldn't that mean that the things that are moving fast because of their distance, are in the past, hence they may be slower in the present? I assumed that the physicists had accounted for that fact in their calculations but I have no one to ask. Thank you for your time. Oh, and I would like to add an observation of mine. Let's assume for the sake of argument that we do live in a multiverse. And if I'm understanding the concept right then each universe has its own value of dark energy, kind of a "luck of the draw situation". A million ways to get it wrong, and only a few to get it right. Wrong being a value of dark energy that can't produce matter, and right being a value like ours that can produce matter. So just as you can describe our planets distance from the sun as being in the "goldilocks zone" You can also use that analogy for which universe we occupy. It seems to follow a pattern.

In the end of lecture 1 on Special Relativity there was a comparison of 2 frames of reference moving in relation to each other. If the relative speed is quite high there would be a difference between t and t1 in the ocasion they meed at the same spot again (suppose one is thavelling on Harley surface and the othjer is me at the Earth fast but with no aceleration). I think I can conclude that for me the voyager would be younger, but can not avoid to thing that he thinks the same of me. On whych lecture I will have the proper answer?

Hello mr. Susskind.Have a question:I wonder why three body problem (in general N body problem)- can not analitically be solved, I mean what is, say in equation of motion (F=ma), preventing us to determine exact solutions to the equation.

Professor Susskind, I woundered what your thoughts are regarding the potential mining of asteroids in our solar system. In light of the 3 body problem , is there a risk that the orbit of the asteroid, other asteroids or even planets may become 'unstable' and is there any realistc way that such effects could be modelled/predicted.

Hello Everyone,I'm a high school junior, and have been watching Prof. Susskind's lectures; currently I'm doing the Quantum Field Theory lectures and I have a quick question. Does anybody know any good books or set of problems (AND solutions) that can teach me group theory sufficiently enough so that I can understand SU(2) and SU(3) well and also do some actual MATH behind the QFT?

hello...I am 16 years years of age, and I have great love for physics.I have a question... in the lectures of special relativity, professor susskind said..I would be using # to represent "fi" (or any field), and ^ and * to represent super-index, and sub-index respectively...#^ has all the normal space components and one positive time component, and #* all normal space components and one negative time component. Then he multipled these two and got a quantity which was invaient.Does that mean that if +ve and -ve time is mixed, then nothing would vary, or in other words, nothing would happen if -ve time goes hand in hand with +ve time...or does that mean that it is applicable to a photon of light, who does not experience any time in order to view the other photon travelling at the same speed of light, with respect to the first photon. Or does invarient here mean something else ?

Hey Susskind, where did you go? Anyways, I think it may be worth looking into the relationship between black holes and the fact the suck everything into a singularity vs. the fact the big bang exploded from a singularity. I'm a professional from NYC, certainly no physicist, but I have a feeling there may be a connection. Has this already been explored?

Suppose we think of black holes as just really small, dense, compact balls of matter. It seems to me that this analogy covers all I've heard of black holes.

I like your analogy of dropping ink into a pool of water and waiting several hours. It shows that, if we had enough computing power, we could track every particle of ink and still theoretically retrieving the information that appears to be lost.

If we apply the ink drop analogy to my definition of a black hole, it seems to me no information would be lost as matter entered the black hole event horizon. That is, it should be theoretically possible to track a particle of matter as it entered the event horizon and crashed into the surface of the small, compact, dense mass. Thus, no information is lost. It just appears to be lost just like the ink drop experiment.